Q.Find the value of $^{100}C_{99}$ :

A combination counts unordered selections — choosing the same set of objects in a different order is not a new outcome. For $n$ distinct objects taken $r$ at a time, $^{n}C_{r} = n!/(r!(n-r)!)$, and it relates to permutations by $^{n}P_{r} = \,^{n}C_{r} \times r!$ (select the group, then separately arrange it). Two properties recur constantly in problems: the symmetry $^{n}C_{r} = \,^{n}C_{n-r}$ (choosing objects to include i …